Factors of 48
48 has 10 factors: 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48. This page shows the pairs that multiply to make 48, its factor tree, the divisibility rules it passes, its multiples and its square root, with the working for each one.
All 10 factors of 48
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10 factors
Strictly, every factor also has a negative twin, because two negative numbers multiply to a positive one. School questions almost always mean the positive factors, which is what this page lists.
- Factor pairs
- 1 × 48, 2 × 24, 3 × 16, 4 × 12 and 6 × 8
- Prime factorization
- 48 = 2⁴ × 3
Why these are the factors of 48
Two numbers form a factor pair of 48 when 48 squares can be arranged into a rectangle with those side lengths and none left over. 48 makes 5 such rectangles, and the factor list is simply their side lengths written down. Tap a pair to build it.
The factor tree of 48
Split 48 into any two factors, then keep splitting until only primes are left. The bottom row gives 48 = 2 × 2 × 2 × 2 × 3. Try a different first split: the tree changes shape, but it always ends on the same primes. Click any circled number to split it another way.
48 = 2 × 2 × 2 × 2 × 3
However you split it, the bottom row stays the same. Every number has exactly one prime factorization.
Divisibility rules, checked against 48
Most factors of 48 can be found without dividing. Each rule below looks at one small part of the number, such as the last digit or the digit sum, and each row shows the exact value the rule checks, so you can verify it yourself.
| Rule | It looks at | Verdict |
|---|---|---|
| 2 | The last digit is even. Here it is 8. | Yes: 48 ÷ 2 = 24 |
| 3 | The digits add up to a multiple of 3. Here they add to 12. | Yes: 48 ÷ 3 = 16 |
| 4 | The last two digits form a multiple of 4. Here they are 48. | Yes: 48 ÷ 4 = 12 |
| 5 | The last digit is 0 or 5. Here it is 8. | No: 48 ÷ 5 leaves remainder 3 |
| 6 | It passes both the 2 rule and the 3 rule. | Yes: 48 ÷ 6 = 8 |
| 7 | Double the last digit and subtract it from the rest. Here that gives -12. | No: 48 ÷ 7 leaves remainder 6 |
| 8 | The last three digits form a multiple of 8. Here they are 48. | Yes: 48 ÷ 8 = 6 |
| 9 | The digits add up to a multiple of 9. Here they add to 12. | No: 48 ÷ 9 leaves remainder 3 |
| 10 | The last digit is 0. Here it is 8. | No: 48 ÷ 10 leaves remainder 8 |
| 11 | Add and subtract the digits alternately from the right. Here that gives 4. | No: 48 ÷ 11 leaves remainder 4 |
Multiples of 48
Multiples run in the other direction: they are the numbers 48 divides into exactly. The list starts 48, 96, 144, 192, 240, 288 and goes on forever, growing by 48 each step. Every multiple of 48 has 48 in its own factor list.
The square root of 48
√48 is not a whole number, because 48 sits between the perfect squares 36 and 49. Its exact simplified form is 4√3: the square factor moves out from under the root sign. The decimal 6.928203 is a rounded approximation, not the exact value.
Everything else about 48
| Even or odd | Even |
|---|---|
| Prime or composite | Composite |
| Number of factors | 10, which matches the rule from 2⁴ × 3: add one to each exponent and multiply. |
| Factors added together | 124 |
| Compared with its own factors | Abundant: the factors below 48 add up to 76, which is more than 48 |
| Numbers below it sharing no factor | 16 of the numbers from 1 to 48 share no factor with 48 |
| 48 squared | 2304 |
| 48 cubed | 110592 |
| A perfect square? | No |
| A perfect cube? | No |
| A triangular number? | No |
| Nearest primes | 47 below, 53 above |
| In binary | 110000 |
| In hexadecimal | 30 |
| As a Roman numeral | XLVIII |
Find the factors of 48 yourself
The answers are hidden here on purpose. Type the factors one at a time; any number that divides 48 exactly counts, including 1 and 48 itself.
Frequently asked questions
- What are the factors of 48?
- 48 has 10 factors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. Each one divides 48 exactly, with no remainder.
- Is 48 a prime number?
- No, 48 is a composite number. It divides exactly by 2 as well as by 1 and itself, which gives it 10 factors in total.
- What is the prime factorization of 48?
- 48 = 2 × 2 × 2 × 2 × 3, which is 2⁴ × 3 in exponent form. Whichever pair you split 48 into first, the factor tree always ends at these same primes.
- What are the factor pairs of 48?
- There are 5: 1 × 48, 2 × 24, 3 × 16, 4 × 12 and 6 × 8. Each pair is a rectangle of 48 squares, with those two numbers as its sides.
- What is the square root of 48?
- √48 is irrational. Its exact simplified form is 4√3; as a decimal it is about 6.928203, which is a rounding rather than the exact value. 48 lies between the perfect squares 36 and 49.
- How many factors does 48 have?
- 10. You can read this off the prime factorization 2⁴ × 3 without listing anything: add one to each exponent and multiply the results.
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